Various attempts have been made to improve the processability of rubber compositions, particularly rubber compositions for pneumatic tires, and the other properties of tires and other products. There is particularly strong need for a rubber composition superior in processability, high in gripping force of the tire, low in heat buildup, and improved in abrasion resistance. For example, Japanese Unexamined Patent Publication (Kokai) No. 62-148544 discloses a rubber composition containing a reinforcing filler and isomaleimide compounded with a natural rubber or synthetic diene rubber, to obtain the improved green strength and green modulus, a low heat buildup and excellent crack growth resistance. Further, Japanese Unexamined Patent Publication (Kokai) No. 7-304305 discloses a pneumatic tire obtained from a composition comprised of rubber in which a mixture of p-phenylene diamine antioxidant, 2,2,4-trimethyl-1,2-dehydroquinoline (or its derivative) and a specific carbon black is compounded, whereby, while maintaining an excellent steering stability and high grip performance, the abrasion resistance is improved. Further, there are needs for a rubber composition superior in processability, high in abrasion resistance when made a tire, and superior in the balance between the high wet braking performance and low rolling resistance. The stabilization of a polymer with a stable free radical is described in Japanese Unexamined Patent Publication (Kokai) No. 8-239510. The effect of preventing rubber deterioration with a stable free radical has been proposed in Japanese Patent Application No. 8-284080. On the other hand, the fact that a reaction of a rubber having a reactive group such as an amino group with a carbon black reduces the hysteresis and decreases the rolling resistance is described in, for example, Japanese Unexamined Patent Publication (Kokai) No. 8-269131. Further, Japanese Unexamined Patent Publication (Kokai) No. 8-283461, Japanese Unexamined Patent Publication (Kokai) No. 8-283462, etc. disclose rubber and carbon black are reacted using thiadiazole or a hydrazide compound, whereby the dispersibility is improved and the heat buildup is reduced.